IMF Staff Papers (2007) 54, 306-337. doi:10.1057/palgrave.imfsp.9450010

A large body of economic literature has focused on the determinants and prediction of debt crises in the aftermath of the severe global turbulence in debt markets in the 1980s. Most studies focus on sovereign defaults and pay little attention to the more basic question, “What is a debt crisis?” This is not surprising given the high frequency of sovereign defaults in this period.

Sovereign defaults are not, however, the only possible outcome of serious foreign debt servicing difficulties. For instance, the period starting with the Mexican “crisis” in 1994-95 has been characterized by turbulent sovereign debt markets and substantial IMF assistance to a number of countries. Yet, according to Moody’s Investors Service (2003), only seven rated sovereign bond issuers have defaulted on their foreign currency-denominated bonds since 1985 and all those defaults happened between 1998 and 2002. The surprisingly low number of sovereign bond defaults by emerging market sovereign borrowers contrasts with the numerous defaults on bank loans in the 1980s.

We argue that defining debt crises solely as sovereign defaults does not take into account the development of international capital markets and, notably, the advent of the bond market for emerging market sovereign issuers. We show how sovereign defaults have become a less reliable indicator of debt-servicing difficulties and suggest a broader indicator of debt-servicing difficulties (debt crisis) that takes into account turbulence in emerging bond markets.

More precisely, we consider events where either there is a sovereign default or secondary market bond spreads are higher than a critical threshold. Using extreme value theory as well as kernel density estimation, we find that the 1,000 basis point (bp) (10 percentage point) threshold corresponds to significant tail events. In practice, market participants often view sovereign bond spreads above the 1,000 bp mark as a signal of turbulence in bond markets.

Formally, we assume that foreign debt-servicing difficulties can be represented by an unobservable latent variable. The standard empirical approach typically uses sovereign defaults as an indicator of debt-servicing difficulties. We argue, however, that sovereign defaults are no longer the appropriate indicator for foreign debt-servicing difficulties, given their rarity since the advent of emerging market bonds. As an alternative, we propose an indicator that complements sovereign defaults with available information from the sovereign bond market. This alternative framework enables us to take into account the development of the bond market for emerging economies in the 1990s and overcome the data limitations owing to the dearth of defaults in the 1990s.

We find that typical theoretical determinants of debt-servicing difficulties—solvency and liquidity measures, as well as macroeconomic control variables—better explain our broader definition of debt crises. In contrast, typical empirical models of debt-servicing problems fail to explain debt crises when they are defined solely as defaults, especially in the period after 1994. In particular, liquidity indicators are significant in explaining our definition of debt crises although they do not play any role in explaining defaults after 1994.

I. Review of the Literature

Episodes of serious foreign debt-servicing difficulties in the 1980s in Latin America and Africa have led to a large body of literature on the determinants of debt crises.¹ These studies typically define debt crises as defaults and study the factors that lead to the nonpayment of pre-agreed debt service (Sachs, 1984).²

A related body of literature focuses on the risk of default and uses spreads between the interest rate charged to a particular country and a benchmark as a proxy for the probability of sovereign default (see Edwards, 1984, for instance). As an alternative, it is possible to determine the probability of default from spreads (see Edwards, 1984; and Duffie and Singleton, 2003) or credit default swaps (Chan-Lau, 2003). Another method uses credit ratings to measure the risk of default (Kaminsky and Schumkler, 2001). Rating downgrades are therefore perceived as an increase in the probability of default, and it is useful to focus on the intensity of rating actions or “rating crises,” as in Jüttner and McCarthy (1998). The probability of sovereign default can also be derived from an estimated transition matrix of the default, as in Hu, Kiesel, and Perraudin (2001).

Sovereign defaults are often associated with other types of financial crises. As a result, some researchers have studied the relevance of sovereign debt variables in explaining financial crises other than debt crises. In Radelet and Sachs (1998) and Rodrik and Velasco (2000), large reversals of capital flows are seen as significant events, whereas in Frankel and Rose (1996); Milesi-Ferretti and Razin (1998); Berg and Pattillo (1999); and Bussière and Mulder (1999) currency crises are considered to be important. In addition, Reinhart (2002) and Sy (2004) study the relationship between defaults and currency crises. Debt-servicing difficulties can, however, manifest themselves in different forms, and a number of recent studies have taken a closer look at the definition of debt crises.

II. The 2002 Brazilian “Debt Crisis”

Events in Brazil, in 2002, illustrate the case of a sovereign that experiences serious debt-servicing difficulties that are not captured by sovereign defaults.⁴ That year, spreads on Brazil’s external bonds rose sharply along with a 40 percent depreciation of the domestic currency, the real. These developments led investors to focus on the impact of the weakness of the real on local debt dynamics, because Brazil’s domestic government debt remained largely indexed to the U.S. dollar and domestic short-term interest rates. The heavily indexed structure of domestic government debt amplified the impact of external shocks, as reflected in rising debt-service costs. With almost one-third of the domestic debt linked to the exchange rate, Brazil’s debt-to-GDP ratio risked rising significantly, potentially leading to a sovereign default.

Against this background, Brazil reached an agreement with the IMF on August 7 that would commit $30 billion in additional financing by the IMF, 80 percent of which would be disbursed during 2003. The program relaxed the previous net international reserve floor. In addition, it ensured fiscal sustainability over the medium term through the maintenance of a primary surplus target of no less than 3.75 percent of GDP during 2003. The fall in Brazilian spreads triggered by the IMF program announcement quickly reversed, however, whereas the real weakened once more to 3.15 per dollar, not far from its all-time low of 3.60 per dollar.

The Brazilian authorities did not default on their large obligation in the bond markets, an option that may have been very costly. Instead, they reached an agreement with the IMF. However, Brazilian bond spreads were consistently above 1,000 bps during this period, indicating the country’s debt-servicing difficulties.

III. A Broader Definition of a Sovereign Debt Crisis

One problem with using sovereign defaults data to proxy for foreign debt-servicing difficulties relates to the dearth of observed post-1994 defaults. In fact, this period is often associated with a number of sovereign credit events in emerging market economies, starting with the Mexican and the Asian “crises” (see Figure 1 and Table 1).

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Comparison Between PesSy and Standard & Poor’s Defaults

(Number of Crises)

Citation: IMF Staff Papers 2007, 003; 10.5089/9781589066502.024.A004

Source: Authors’ calculations.Note: “StdD” stands for defaults as defined by Standard & Poor’s defaults. “PesSy” refers to events when there is either a default as defined by Standard & Poor’s or sovereign bond spreads are above 1,000 bps (10 percentage points).

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Table 1.

Number of Crises, by Definition

Source: Authors’ calculations. Note: Defaults refer to default events as defined by Standard & Poor’s. PesSy refers to events when there is either a default as defined by Standard and Poor’s or when secondary market sovereign bond spreads are higher than 1,000 bps (10 percentage points).

Table 1.

Number of Crises, by Definition

	Total Observations	Percentage	Number of Crises
Defaults (1975-2002)	886	24	214
PesSy (1975-2002)	886	27	238
Defaults (1994-2002)	287	16	46
PesSy (1994-2002)	287	24	70
Defaults (1975-93)	599	28	168

Source: Authors’ calculations. Note: Defaults refer to default events as defined by Standard & Poor’s. PesSy refers to events when there is either a default as defined by Standard and Poor’s or when secondary market sovereign bond spreads are higher than 1,000 bps (10 percentage points).

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Table 1.

Number of Crises, by Definition

	Total Observations	Percentage	Number of Crises
Defaults (1975-2002)	886	24	214
PesSy (1975-2002)	886	27	238
Defaults (1994-2002)	287	16	46
PesSy (1994-2002)	287	24	70
Defaults (1975-93)	599	28	168

Source: Authors’ calculations. Note: Defaults refer to default events as defined by Standard & Poor’s. PesSy refers to events when there is either a default as defined by Standard and Poor’s or when secondary market sovereign bond spreads are higher than 1,000 bps (10 percentage points).

Our concern that defaults are not a measure subtle enough to capture changes in the nature of debt-servicing difficulties and the evolution of international capital markets is shared by other authors. For instance, MRS propose that defaults be complemented with events during which a sovereign receives substantial IMF assistance.

IMF bailouts, however, do not show a structural change between the two periods before and after 1994. In fact, the percentage of countries receiving IMF assistance of more than 100 percent of quota has barely increased, to 4.8 percent post-1994 from 4.5 percent in the previous period. Moreover, the percentage of countries receiving IMF bailouts without defaulting has barely increased, to 36 percent post-1994 from 32 percent in the previous period.⁵ In other words, although the MRS methodology of complementing default events with IMF bailouts increases the total number of crisis events, it does not change the relative number of crises per period—that is, the ratio of the number of crisis events in the 1980s to the number of crisis events in the 1990s. So we are still left with the puzzle of a drastic drop in debt crises post-1994.

A possible explanation for the rarity of post-1994 default events could be that the determinants of defaults improved in the 1990s relative to their earlier levels. If so, the factors that successfully explained defaults in the 1970s and 1980s should have no problem predicting the reduced number of defaults in the 1990s. Our regression results show, however, that this may not be the case. Empirical models of debt crises that worked well until the 1980s cannot explain the few default events in the 1990s and instead predict a greater number of such events.

It is also possible that there was a structural break between the regressors and the dependent debt crisis variables. Such a break could be attributed to the development of international financial markets in the 1990s. In this case, we should expect that models estimated for the 1970s and 1980s would no longer work for the 1990s. We will, however, show that this may not be the case, although we believe that financial development deserves closer examination. In particular, we will attempt to show that the rapid development of the sovereign bond market for emerging economies can be used to obtain a relevant definition of debt crises.

We start from the following simple consideration. The more emerging countries have gained access to sovereign bond markets, the more they have reduced the share of bank loan debt to total debt. This means that defaulting could be associated with both forms of debt contracts but also with only one of them. So as a first step it seems sensible to proxy for foreign debt-servicing difficulties using bank loans, bonds, or both types of debt instruments.

A second consideration is that very few countries have defaulted on their foreign bonds in the post-1994 period. As a result, the usual definition of bond default must be one that is not subtle enough to capture the wide range of debt-servicing difficulties. The anonymous structure of bond markets makes renegotiation more difficult for bond contracts than bank loans. Renegotiation, however, is one of the most common credit events for other types of debt contracts such as bank loans and is a clear sign of debt-servicing difficulties. In contrast, we are likely to miss important periods of debt-servicing difficulties when we restrict ourselves to the usual definition of default, because of the difficulty of renegotiating bond contracts.

In order to overcome this problem, we add a market-oriented measure of debt-servicing difficulties based on sovereign bond spreads: a debt crisis happens when there is either a default as defined by rating agencies (in this case S&P) or when the secondary market sovereign bond spreads are higher than a critical threshold. For simplicity we will refer to debt crises defined as above as the PesSy indicator of foreign debt-servicing difficulties.

Presumably, spreads on foreign currency-denominated sovereign bonds may be part of a broader set of measures of macroeconomic or financial conditions that characterize the ability and willingness of a sovereign borrower to repay its debt. However, there are advantages in using sovereign bond spreads, given the high frequency and quality of the data as well as the simplicity in distinguishing among entry, continuation, and exit from a crisis.

Because they provide market information, however, sovereign bond spreads are not immune from possible overreaction from market participants. Hence, bond spreads could be, at times, misaligned with economic fundamentals and rather reflect market participants’ overreactions to new information about the borrower. Our crisis indicator would therefore capture a credit event, whether it is due to economic imbalances or market overreactions. From a policy perspective, however, both types of events are important and have to be managed to avoid negative spillover effects in the economy. For instance, Dailami, Masson, and Padou (2005) model the probability of sovereign default so that it (1) depends on stock of debt as well as lagged income, (2) is highly nonlinear, and (3) can have multiple solutions. Their intuition is that by expecting a default, investors can make a default more likely. However, this is true in only certain ranges for the variables and the parameters. In particular, debt has to be large enough that increases in interest costs can make debt service painful for the emerging market borrower. Because of the existence of multiple equilibria, the effect of explanatory variables on spreads is different, depending on which equilibrium is chosen.⁶

High interest rate increases also may not be attributed solely to debt-servicing problems. For instance, Garcia and Rigobon (2004) compute events during which the probability of the simulated debt-to-GDP ratio exceeds a threshold deemed risky. These authors find that such “risk probabilities” are closely correlated to sovereign spreads. In this type of framework, the relevant variables do not have independent paths, and high interest rates can occur because of the co-movement observed in the variables of interest and debt dynamics. For instance, the authors find that, as is typically the case for emerging markets, a recession can cause the fiscal accounts to deteriorate, the real interest rate and inflation to rise, and the exchange rate to fall. Such debt dynamics worsen when the sovereign debt is dollar denominated.

Figure 1 shows the number of crises signaled by defaults—as defined by S&P—and by our crisis indicator.⁷ In Table 1, we divide the overall sample—which goes from 1975 to 2002—into two subsamples ranging from 1975 to 1993 and from 1994 to 2002. The data show a dramatic drop in the number of defaults to 16 percent of total observations in the 1994-2002 period, from 28 percent in the 1975-93 period. In contrast, our proxy for sovereign debt-servicing difficulties indicates more stable behavior with a proportion of 24 percent of debt crises in the 1994-2002 period.

In order to formalize the previous argument and compare the two definitions of debt crises—namely, sovereign defaults and the indicator of debt-servicing difficulties (PesSy), we assume that there is an unobservable state of nature that corresponds to a country experiencing foreign debt-servicing difficulties. These foreign debt-servicing difficulties are not observable per se by creditors,⁸ but the observation of some indicators, such as the inability of a sovereign to repay its debt, may be used to infer the true state of affairs.

We assume the existence of a latent variable, y*, that represents foreign debt-servicing difficulties for a particular country. The underlying response variable is then defined by a regression relationship:

The next step is to link the latent variable to some observable variables. The standard approach is to use sovereign defaults as an indicator of debt-servicing difficulties. Thus, the default indicator I is defined as

In contrast, it is possible to use the information from the bond market and assume that a sovereign credit event is also signaled when a country’s bond spreads, s, cross a threshold, τ. We define the spreads in excess of the threshold as

where h is any strictly increasing Borel function defined on the y* probability space, such that h(0) = 0. We then construct a binary indicator related to the latent variable, S, such as

We propose a more general model combining the default indicator with the spreads-based indicator, so that a debt crisis occurs when either a default exists or bond spreads are above a threshold. In this case, the latent variable is linked to a bivariate observable variable, ${\tilde{y}}_t\equiv (I_t,S_t),$ such that

which can be reduced to the following univariate variable:

If specification (4a)-(4b) is the “true” model, then models (2) and (3) are misspecified. Furthermore, using model (2) implies assuming that the conditional probability is unconditional. From model (2) we get

From model (4) we have

Until the beginning of the 1990s, conditioning on S= 0 was consistent with the fact that most emerging economies did not have access to international bond markets. In contrast, it seems reasonable to assume that such a specification may miss the information given by bond markets, because emerging markets are gradually using sovereign bonds as a major source of funding. We therefore complement the typical default indicator with an indicator that uses the information from international bond markets.

As an alternative, our proposed indicator assumes that there has been historically no structural break between the latent variable and the covariates. Rather, there have been difficulties in choosing a proper indicator of an unobservable dependent variable. In the next section, we use statistical methods to estimate the critical threshold for bond spreads, τ.

Estimating the Threshold for Bond Spreads Using Extreme Value Theory

Sovereign bond spreads, like most financial series, are not typically distributed. Instead, bond spreads are characterized by extreme observations or fat tails and volatility clustering. We can use extremal analysis to capture extreme events, which we define as debt crises. Extremal analysis has in addition the advantage of using nonparametric methods rather than assuming a particular distribution for bond spreads.

Our approach is similar to that in a number of studies that attempt to capture extreme events in the foreign exchange markets, such as Hols and de Vries (1991); Koedijk, Stork, and de Vries (1992); and Pozo and Amuedo-Dorantes (2003). Typically, studies using extreme value theory focus on the estimation of a tail parameter α or alternatively on the inverse of the tail parameter, γ = 1/α, by use of the nonparametric Hill estimator. This requires stationary and serially uncorrelated data. Our bond spread series are clearly stationary, at all frequencies, but are not serially uncorrelated at high frequency (daily and monthly). As a result, we focus on annual data (see the Appendix).

We pool the data and rank-order the observations from the lowest to the highest, S₁ … S_n, in order to compute the following measure of the tail parameter:

$1/\hat{\alpha }=\hat{\gamma }=\frac{1}{m}\underset{i=0}{\overset{m}{\mathrm{\Sigma }}}\ln (S_{n-1}/S_{n-m})\mathrm{.}$

The key point in the estimation of the critical bond spread threshold is the choice of the variable m, where $\hat{\gamma }$ is stable. We therefore use Hill plots to estimate the values of $\hat{\gamma }$ against possible values of m. To verify that we have identified stabilization in the behavior of $\hat{\gamma }$ we also use recursive least squares to regress $\hat{\gamma }$ on a time trend and a constant, successively adding observations and obtaining a one-step-ahead forecast with the respective 90 percent confidence interval (see the Appendix).

For the yearly sample we find that a value of m between 42 and 50 makes the parameter 1/$\hat{\alpha }$ relatively stable. Using the above relationship, m = 42 leads to a value of 1,072 bps and m = 50 to 969 bps. Because the relationship between m and the extreme value threshold is clearly monotonic, we conclude that our threshold reasonably lies between 969 and 1,072 bps (see Table A2).

We also assess the extent to which the threshold for bond spreads estimated using extreme value theory would affect the construction of the binary crisis dependent variable. Table 2, which uses the 1,000 bps mark, shows that the use of a critical threshold from extreme value estimation does not significantly change the classification of the data in crisis periods. Using the upper estimation, we add 2.3 percent crisis periods and using the lower estimation we ignore 1.4 percent crisis events with respect to the total number of crises (Table 2).

Table 2.

Extreme Value Theory (EVT) vs. 1,000 bps Thresholds

(Sample: 1994-2002)

Source: Authors’ calculations. Note: The abbreviation bps denotes basis points (hundredths of a percentage).

Table 2.

Extreme Value Theory (EVT) vs. 1,000 bps Thresholds

(Sample: 1994-2002)

	Matching	EVT Adding	EVT Crossing Out	Total
Total number	[211, 213]	[5, 0]	[0, 3]	216
As percentage	[0.98, 0.99]	[0, 0.023]	[0, 0.014]	1

Source: Authors’ calculations. Note: The abbreviation bps denotes basis points (hundredths of a percentage).

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Table 2.

Extreme Value Theory (EVT) vs. 1,000 bps Thresholds

(Sample: 1994-2002)

	Matching	EVT Adding	EVT Crossing Out	Total
Total number	[211, 213]	[5, 0]	[0, 3]	216
As percentage	[0.98, 0.99]	[0, 0.023]	[0, 0.014]	1

Source: Authors’ calculations. Note: The abbreviation bps denotes basis points (hundredths of a percentage).

We find that the estimated values for the critical bond spread threshold are consistent with anecdotal evidence (the 1,000 bps mark is between the lower and upper estimate) and do not significantly affect our dependent binary variable. In the next section, we take a second look at the data using kernel density estimation.

Estimating the Threshold for Bond Spreads Using a Kernel Density Estimation

As discussed above, sovereign bond spread series do not follow a typical distribution. In this section, we use kernel density estimation as an alternative to extremal analysis to estimate the key features of our sovereign bond spread series. We are particularly interested in the possible existence of modes around high spread values. If bond spreads tend to cluster around some low and large observations, then we can use these values to define “tranquil” and “crisis” periods.

Intuitively, whenever spreads are close to a limit that cannot be passed smoothly, the observations will concentrate around it until the limit is finally passed or the surging pressure reduced. Because the body of the distribution lies to the left of our threshold we also should expect that the mode is slightly on the left (see Section II of the Appendix for an illustration).

We analyze both yearly and daily data. In this case, the presence of autocorrelation, which is very strong for daily data, does not spoil the results. In a univariate sample that is not identically and independently distributed but autocorrelated, we expect its histogram to show a mode for each relevant turning point, and in this case around tranquil and crisis periods. In addition, there may be smaller modes for very high spreads that have been peaks or turning points for some countries.

The kernel density estimation confirms the assumption that there is a mode for tranquil and crisis periods. In particular, we find a mode around 1,000 bps for both daily and yearly data. Because the yearly data are not correlated, we also fit a gamma and a Weibul distribution (an extreme value distribution) to estimate the 90th percentile.⁹ We choose the 90th percentile as a proxy for extreme events. Our results indicate that the 1,000 bp threshold is inside the 95 percent confidence bands for the 90th percentile of the fitted distribution (Table 3).

Table 3.

Thresholds for Bond Spreads from Kernel Density Estimations

Source: Authors’ calculations. Note: bps = basis points.

Table 3.

Thresholds for Bond Spreads from Kernel Density Estimations

Estimated 90th Percentile—95 Percent Confidence Interval
Gamma distribution	1,036.52	[980.55, 1,093.85]
Weibul distribution	978.82	[795.10, 1,248.05]
Percentile Corresponding to 1,000 bps
Gamma distribution	0.88
Weibul distribution	0.91

Source: Authors’ calculations. Note: bps = basis points.

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Table 3.

Thresholds for Bond Spreads from Kernel Density Estimations

Estimated 90th Percentile—95 Percent Confidence Interval
Gamma distribution	1,036.52	[980.55, 1,093.85]
Weibul distribution	978.82	[795.10, 1,248.05]
Percentile Corresponding to 1,000 bps
Gamma distribution	0.88
Weibul distribution	0.91

Source: Authors’ calculations. Note: bps = basis points.

Psychological/Market Threshold

Sovereign bond market participants typically consider the 1,000 bps mark for spreads a critical psychological threshold. Indeed, discussions with market participants suggest that price quotes are increasingly based on expected recovery values in case of a default, when bond spreads cross the 1,000 bps mark.

For instance, Altman (1998) defines distressed securities as those publicly held and traded debt and equity securities of firms that have defaulted on their debt obligations and/or have filed for protection under Chapter 11 of the U.S. Bankruptcy Code. Under a more comprehensive definition, Altman (1998) considers that distressed securities would include those publicly held debt securities selling at sufficiently discounted prices so as to be yielding, should they not default, a significant premium of a minimum of 1,000 bps (or 10 percent) over comparable U.S. Treasury securities. Similarly, some market participants consider securities to have reached distressed levels when they have lost one-third of their value.

The sections above corroborate the existence of a 1,000 bps market threshold. Table 4 presents the debt crisis dates for both the standard default definition (S&P) and our broader indicator (PesSy) in the period 1994-2002. Prior to 1994, both indicators coincide, because the bond market for emerging economies was not developed. In the next sections, we use the framework developed above to estimate econometric models of debt crises.

Table 4.

Debt Crises Dates, 1994-2002

Source: Standard & Poor’s and authors’ calculations. Note: S&P = Standard & Poor’s.

¹Default or bond spreads above 1,000 bps.

Table 4.

Debt Crises Dates, 1994-2002

Country	PesSy1	Default (S&P)
Algeria	1994-96, 1999	1994-96
Argentina	1995, 2001-02	2001-02
Brazil	1994-95, 1999, 2002	1994
Côte d’Ivoire	1994-2002	1994-98, 2000-02
Chile	No crisis	No crisis
China	No crisis	No crisis
Colombia	No crisis	No crisis
Dominican Rep.	1994	1994
Ecuador	1994-96, 1998-2002	1994-95, 1999-2000
Egypt	No crisis	No crisis
El Salvador	No crisis	No crisis
Hungary	No crisis	No crisis
Indonesia	1998-2000, 2002	1998-2000, 2002
Korea	No crisis	No crisis
Lebanon	No crisis	No crisis
Malaysia	1995	No crisis
Mexico	1995	No crisis
Morocco	No crisis	No crisis
Nigeria	1994-96, 1999-2002	No crisis
Pakistan	1998-99, 2001	1998-99
Panama	1994-96	1994-96
Peru	1994-97	1994-97
Philippines	No crisis	No crisis
Poland	1994	1994
Russia	1994-2000	1994-2000
South Africa	No crisis	No crisis
Thailand	No crisis	No crisis
Tunisia	No crisis	No crisis
Turkey	No crisis	No crisis
Ukraine	1998-2001	1998-2000
Uruguay	No crisis	No crisis
Venezuela	1994-97,1999, 2002	1995-97

Source: Standard & Poor’s and authors’ calculations. Note: S&P = Standard & Poor’s.

¹Default or bond spreads above 1,000 bps.

View Table

Table 4.

Debt Crises Dates, 1994-2002

Country	PesSy1	Default (S&P)
Algeria	1994-96, 1999	1994-96
Argentina	1995, 2001-02	2001-02
Brazil	1994-95, 1999, 2002	1994
Côte d’Ivoire	1994-2002	1994-98, 2000-02
Chile	No crisis	No crisis
China	No crisis	No crisis
Colombia	No crisis	No crisis
Dominican Rep.	1994	1994
Ecuador	1994-96, 1998-2002	1994-95, 1999-2000
Egypt	No crisis	No crisis
El Salvador	No crisis	No crisis
Hungary	No crisis	No crisis
Indonesia	1998-2000, 2002	1998-2000, 2002
Korea	No crisis	No crisis
Lebanon	No crisis	No crisis
Malaysia	1995	No crisis
Mexico	1995	No crisis
Morocco	No crisis	No crisis
Nigeria	1994-96, 1999-2002	No crisis
Pakistan	1998-99, 2001	1998-99
Panama	1994-96	1994-96
Peru	1994-97	1994-97
Philippines	No crisis	No crisis
Poland	1994	1994
Russia	1994-2000	1994-2000
South Africa	No crisis	No crisis
Thailand	No crisis	No crisis
Tunisia	No crisis	No crisis
Turkey	No crisis	No crisis
Ukraine	1998-2001	1998-2000
Uruguay	No crisis	No crisis
Venezuela	1994-97,1999, 2002	1995-97

Source: Standard & Poor’s and authors’ calculations. Note: S&P = Standard & Poor’s.

¹Default or bond spreads above 1,000 bps.

IV. Defaults vs. Market-Based Definition of Debt Crises (PesSy)

In this section, we investigate whether the typical determinants of debt crises found in the literature are significant when we broaden the definition of debt crises to include information from the bond markets. We also study how well these explanatory variables forecast our proposed broader definition of debt crises. As an illustration, we also repeat the same exercise for sovereign defaults.

Baseline Regressions, 1975-2002

The theoretical and empirical literature has highlighted a number of variables that help predict sovereign defaults. The explanatory variables usually include (1) liquidity indicators (short-term debt over reserves; or short-term debt, debt service due, and reserves separately); (2) variables that measure the magnitude and structure of external debt; and (3) macroeconomic control variables, such as measures of openness and real exchange rate over-valuation.

For instance, MRS, after reviewing the empirical and theoretical literature on debt crises, emphasize the following determinants of debt crises:

• solvency measures, such as public and external debt relative to capacity to pay;

• liquidity measures, such as short-term external debt and external debt service, possibly in relation to reserves or exports;

• currency crisis (early-warning systems) variables;

• external volatility and volatility in economic policy measures;

• macroeconomic control variables, such as growth, inflation, and exchange rate; and

• political and institutional variables that capture a country’s willingness to pay.

We follow the literature and use the typical determinants of debt crises as explanatory variables. In fact, we assume that standard explanatory variables are the correct ones in predicting debt crises but that indicators of debt crises may be inaccurate.

As a first descriptive step we use the whole sample from 1975 to 2002. In Table 5, we show the estimation results for the standard framework—where the sovereign default variable is the indicator variable for debt crises. In Table 6, we present the results for the alternative market-based indicator (PesSy).¹⁰

Table 5.

Regression Results Using Default Definition, 1975-2002

Source: Authors’ calculations. Note: GEE logit population-averaged model, correlation exchangeable, Huber-White estimator. 567 observations. CI refers to the confidence intervals.

Table 5.

Regression Results Using Default Definition, 1975-2002

S&P Default					95 Percent					95 Percent
	Definition	Coeff.	Z	P>|z|	CI		Coeff.	Z	P>|z|	CI
Openness		-0.05	-3.14	0.00	-0.08	-0.02	-0.05	-3.08	0.00	-0.07	-0.02
Overvaluation		0.01	3.40	0.00	0.01	0.02	0.01	3.37	0.00	0.00	0.02
Total debt		0.06	3.57	0.00	0.03	0.09	0.06	3.56	0.00	0.03	0.09
	over GDP
Short-term		0.19	2.07	0.04	0.01	0.36	0.19	2.05	0.04	0.01	0.37
	debt over
	reserves
Real growth		-0.08	-2.49	0.01	-0.15	-0.02	-0.08	-2.35	0.02	-0.15	-0.01
	rate
Inflation							0.00	2.67	0.01	0.00	0.00
Constant		-1.94	-2.43	0.02	-3.51	-0.37	-2.09	-2.48	0.01	-3.74	-0.44
Wald x2 (5)		44.0					46.1
	and (6)

Source: Authors’ calculations. Note: GEE logit population-averaged model, correlation exchangeable, Huber-White estimator. 567 observations. CI refers to the confidence intervals.

View Table

Table 5.

Regression Results Using Default Definition, 1975-2002

S&P Default					95 Percent					95 Percent
	Definition	Coeff.	Z	P>|z|	CI		Coeff.	Z	P>|z|	CI
Openness		-0.05	-3.14	0.00	-0.08	-0.02	-0.05	-3.08	0.00	-0.07	-0.02
Overvaluation		0.01	3.40	0.00	0.01	0.02	0.01	3.37	0.00	0.00	0.02
Total debt		0.06	3.57	0.00	0.03	0.09	0.06	3.56	0.00	0.03	0.09
	over GDP
Short-term		0.19	2.07	0.04	0.01	0.36	0.19	2.05	0.04	0.01	0.37
	debt over
	reserves
Real growth		-0.08	-2.49	0.01	-0.15	-0.02	-0.08	-2.35	0.02	-0.15	-0.01
	rate
Inflation							0.00	2.67	0.01	0.00	0.00
Constant		-1.94	-2.43	0.02	-3.51	-0.37	-2.09	-2.48	0.01	-3.74	-0.44
Wald x2 (5)		44.0					46.1
	and (6)

Source: Authors’ calculations. Note: GEE logit population-averaged model, correlation exchangeable, Huber-White estimator. 567 observations. CI refers to the confidence intervals.

Table 6.

Regression Results Using PesSy Indicator, 1975-2002

Source: Authors’ calculations. Note: GEE logit population-averaged model, correlation exchangeable, Huber-White estimation. 567 observations. CI refers to confidence intervals.

Table 6.

Regression Results Using PesSy Indicator, 1975-2002

PesSy					95 Percent					95 Percent
	Indicator	Coeff.	Z	P>|z|	CI		Coeff.	Z	P>|z|	CI
Openness		-0.03	-2.06	0.04	-0.07	0.00	-0.03	-2.15	0.03	-0.06	0.00
Overvaluation		0.01	2.75	0.01	0.00	0.02	0.01	2.41	0.02	0.00	0.01
Total debt		0.06	4.26	0.00	0.03	0.09	0.06	4.46	0.00	0.03	0.09
	over GDP
Short-term		0.30	2.50	0.01	0.06	0.53	0.30	2.47	0.01	0.06	0.53
	debt over
	reserves
Real growth		-0.09	-2.61	0.01	-0.17	-0.02	-0.08	-2.29	0.02	-0.15	-0.01
	rate
Inflation							0.00	1.25	0.21	0.00	0.01
Constant		-2.80	-4.01	0.00	-4.18	-1.43	-3.08	-4.99	0.00	-4.29	-1.87
Wald x2 (5)		48.0					45.4
	and (6)

Source: Authors’ calculations. Note: GEE logit population-averaged model, correlation exchangeable, Huber-White estimation. 567 observations. CI refers to confidence intervals.

View Table

Table 6.

Regression Results Using PesSy Indicator, 1975-2002

PesSy					95 Percent					95 Percent
	Indicator	Coeff.	Z	P>|z|	CI		Coeff.	Z	P>|z|	CI
Openness		-0.03	-2.06	0.04	-0.07	0.00	-0.03	-2.15	0.03	-0.06	0.00
Overvaluation		0.01	2.75	0.01	0.00	0.02	0.01	2.41	0.02	0.00	0.01
Total debt		0.06	4.26	0.00	0.03	0.09	0.06	4.46	0.00	0.03	0.09
	over GDP
Short-term		0.30	2.50	0.01	0.06	0.53	0.30	2.47	0.01	0.06	0.53
	debt over
	reserves
Real growth		-0.09	-2.61	0.01	-0.17	-0.02	-0.08	-2.29	0.02	-0.15	-0.01
	rate
Inflation							0.00	1.25	0.21	0.00	0.01
Constant		-2.80	-4.01	0.00	-4.18	-1.43	-3.08	-4.99	0.00	-4.29	-1.87
Wald x2 (5)		48.0					45.4
	and (6)

Source: Authors’ calculations. Note: GEE logit population-averaged model, correlation exchangeable, Huber-White estimation. 567 observations. CI refers to confidence intervals.

We find that, for the 1975-2002 period, solvency measures (total debt over GDP) and liquidity indicators (short-term debt over reserves) are statistically significant in explaining debt crises, independently of how they are defined. However, the liquidity indicator (short-term debt over reserves) plays a more important role; inflation is not significant when the market-based indicator is used. Other macroeconomic control variables—in particular, real growth rate, inflation, and real exchange rate overvaluation—are also important in explaining crises, as is a measure of openness (imports plus exports over GDP). All regressors are significant at 5 percent in both specifications (with or without inflation) and enter with the right sign.

Finally, a comparison of the Wald statistics suggests that standard macro variables, except for inflation, provide a better explanation of debt crises as defined by the market-based indicator (PesSy).

Out-of-Sample Comparisons

Typically, model estimation attempts to find the explanatory variables that better explain a particular dependent variable. In this section, we take the explanatory variables as given and focus instead on finding the better proxy for the unobservable dependent variable, debt-servicing difficulties. We show that debt-servicing difficulties are better captured when we use information from both sovereign defaults and bond markets.

The two indicators of debt-servicing difficulties coincide in the period before 1994—that is, before the advent of the emerging bond market—and differ only afterward. We therefore estimate the model for the period 1975-93 to forecast debt crises in 1994-2002 (out-of-sample). We then compare our forecasts with actual proxies of the dependent variable in 1994-2002. We find that forecasted debt crises are statistically closer to the actual observations of our market-based indicator than sovereign defaults.

Estimation results for the subsample 1975-93 are shown in Table 7.¹¹ All variables are significant except for inflation, and the Wald statistic is comparable to the values obtained earlier. The solvency (total debt over GDP) and liquidity (short-term debt over reserves) variables play a bigger role compared with the results obtained using the whole sample with the default indicator. The opposite is true for inflation, which is now insignificant. In other words, the estimation results for the 1975-93 period seem to be comparable to the results obtained with the market-based indicator for the whole sample period (1975-2002) (compare Table 7 to Table 6 and Table 5).

Table 7.

Regression Results, Subsample for 1975-93

(Common Framework)

Source: Authors’ calculations. Notes: GEE logit population-averaged model, correlation exchangeable, Huber-White estimation. 360 observations. CI refers to confidence intervals.

Table 7.

Regression Results, Subsample for 1975-93

(Common Framework)

S&P Default Definition					95 Percent
	= PesSy Indicator	Coeff.	Z	P>|z|	CI
Openness		-0.04	-2.92	0.00	-0.07	-0.01
Overvaluation		0.01	2.27	0.02	0.00	0.02
Total debt over GDP		0.07	4.05	0.00	0.03	0.10
Short-term debt over reserves		0.23	1.97	0.05	0.00	0.46
Real growth rate		-0.09	-1.93	0.05	-0.17	0.00
Inflation		0.00	0.88	0.38	0.00	0.01
Constant		-2.37	-4.29	0.00	-3.45	-1.29
Wald x2 (6)		39.20

Source: Authors’ calculations. Notes: GEE logit population-averaged model, correlation exchangeable, Huber-White estimation. 360 observations. CI refers to confidence intervals.

View Table

Table 7.

Regression Results, Subsample for 1975-93

(Common Framework)

S&P Default Definition					95 Percent
	= PesSy Indicator	Coeff.	Z	P>|z|	CI
Openness		-0.04	-2.92	0.00	-0.07	-0.01
Overvaluation		0.01	2.27	0.02	0.00	0.02
Total debt over GDP		0.07	4.05	0.00	0.03	0.10
Short-term debt over reserves		0.23	1.97	0.05	0.00	0.46
Real growth rate		-0.09	-1.93	0.05	-0.17	0.00
Inflation		0.00	0.88	0.38	0.00	0.01
Constant		-2.37	-4.29	0.00	-3.45	-1.29
Wald x2 (6)		39.20

Source: Authors’ calculations. Notes: GEE logit population-averaged model, correlation exchangeable, Huber-White estimation. 360 observations. CI refers to confidence intervals.

Given that we estimate a binary variable model, we follow the early-warning indicator literature for currency crises and estimate the number of matched crises (A), false alarms (B), missing crises (C), and matched tranquil periods (D).¹²

In this framework, a signal is sent whenever the estimated probability of a crisis crosses a given threshold, T. Typically, the threshold is set to be equal to the unconditional probability of a crisis occurring. Because we are trying to match the crisis events, there is no clear reason for setting T to the unconditional probability, and we instead leave the variables A, B, C, and D as a function of the threshold T, which is optimally determined. In order to calculate the optimal threshold value for issuing a warning, T*, we minimize the following noise-to-signal ratio: L(T) = B(T)/A(T) + C(T)/D(T). Because the standard error for the forecasts is quite high, we estimate the values for T* using a bootstrapping method, and hence for A(T*), B(T*), C(T*), D(T*), and L(T*). Table 8 shows the ratios for “Matched Crises over Total Crises,” A(T*)/[A(T*) + C(T*)], and “False Alarms over Tranquil Periods,” B(T*)/ [B(T*) + D(T *)].

Table 8.

Matched Crises over Total Crises, and False Alarms over Tranquil Periods

Source: Authors’ calculations. Note: The in-sample point estimation refers to the estimated parameters without bootstrapping; 90 percent confidence intervals are in brackets; S&P = Standard & Poor’s.

Table 8.

Matched Crises over Total Crises, and False Alarms over Tranquil Periods

	Matched Crises over	False Alarms over
	Total Crises	Tranquil Periods
S&P defaults	0.43 [0.33, 0.50]	[0.12, 0.13]
PesSy	0.61 [0.55, 0.67]	[0.19, 0.20]
In sample (point estimate)	0.86	0.14
In sample	0.69 [0.52, 0.91]	[0.02, 0.20]

Source: Authors’ calculations. Note: The in-sample point estimation refers to the estimated parameters without bootstrapping; 90 percent confidence intervals are in brackets; S&P = Standard & Poor’s.

View Table

Table 8.

Matched Crises over Total Crises, and False Alarms over Tranquil Periods

	Matched Crises over	False Alarms over
	Total Crises	Tranquil Periods
S&P defaults	0.43 [0.33, 0.50]	[0.12, 0.13]
PesSy	0.61 [0.55, 0.67]	[0.19, 0.20]
In sample (point estimate)	0.86	0.14
In sample	0.69 [0.52, 0.91]	[0.02, 0.20]

Source: Authors’ calculations. Note: The in-sample point estimation refers to the estimated parameters without bootstrapping; 90 percent confidence intervals are in brackets; S&P = Standard & Poor’s.

The results, shown in Table 8, indicate that, in terms of matched crises, the typical determinants of debt crises forecast better the market-based indicator (PesSy) than sovereign defaults. This is not really surprising given that there are more debt crises under the market-based definition than defaults. Hence, for a more conclusive answer and to aggregate the previous results, we introduce a loss function—also in this case taken from the early-warning-indicator literature. The loss function equals the weighted sum of false alarms (as a share of total tranquil periods) and missed crises (as a share of total crisis periods).¹³

Results are shown in Table 9. The S&P defaults-associated “loss” is, with a 90 percent confidence, within 1.13 and 2.14, whereas the loss associated with the market-based indicator is between 0.75 and 1.07.¹⁴

Table 9.

Bootstrapped Results for Standard and PesSy Distress Definition Loss Function

(10th percentile, mean value, 90th percentile for the loss function)

Source: Authors’ calculations.

Table 9.

Bootstrapped Results for Standard and PesSy Distress Definition Loss Function

(10th percentile, mean value, 90th percentile for the loss function)

	Mean and CI
Default definition loss (out of sample)	1.50 [1.13-2.14]
Associated optimal threshold	0.34 [0.23 and 0.28]
PesSy definition loss (out of sample)	0.89 [0.75, 1.07]
Associated optimal threshold	0.32 [0.38 and 0.36]
In-sample result loss	0.39
In-sample result optimal threshold:	0.57

Source: Authors’ calculations.

View Table

Table 9.

Bootstrapped Results for Standard and PesSy Distress Definition Loss Function

(10th percentile, mean value, 90th percentile for the loss function)

	Mean and CI
Default definition loss (out of sample)	1.50 [1.13-2.14]
Associated optimal threshold	0.34 [0.23 and 0.28]
PesSy definition loss (out of sample)	0.89 [0.75, 1.07]
Associated optimal threshold	0.32 [0.38 and 0.36]
In-sample result loss	0.39
In-sample result optimal threshold:	0.57

Source: Authors’ calculations.

These results support the idea that defining debt crises solely as defaults is too strict to capture debt-servicing difficulties in the 1990s. In addition, we do not find evidence of a structural break for the usual macro determinants in 1994 stemming from the advent of the bond market for emerging economies. Instead, we find that the model estimated in the 1975-93 period still predicts debt crises quite well in the 1994-2002 period, provided debt crises are broadly defined to include both defaults and events when bond spreads are above 1,000 bps. In contrast, the model does not predict sovereign defaults well in the 1994-2002 period.

1994-2002: A New Decade

Finally, we illustrate the robustness of the model in the period after 1994, rather than for the whole sample, because this period is characterized by the growth of the emerging bond markets.

We estimate the model for the 1994-2002 subsample and find that, without inflation, the Wald statistic is 29.4 when debt crises include information from the bond market, and 8.4 when sovereign defaults are used. When inflation is considered as a regressor, the Wald statistics are 59.5 and 41.6, respectively. Real growth and openness variables are not as significant as before, whereas inflation is strongly significant in both setups.

More interesting, the liquidity variable (short-term debt over reserves) does not play any role in the 1994-2002 period when debt crises are defined as defaults. In contrast, it is significant and has the right sign when debt crises are defined to include turbulence in bond markets. Results are shown in Tables 10 and 11.

Table 10.

Regression Results Using Default Definition, Subsample for 1994-2002

Source: Authors’ calculations. Note: GEE logit population-averaged model, correlation exchangeable, Huber-White estimation. 207 observations. CI refers to confidence intervals.

Table 10.

Regression Results Using Default Definition, Subsample for 1994-2002

					95 Percent					95 Percent
Defaults		Coeff.	Z	P>|z|	CI		Coeff.	Z	P>|z|	CI
Openness		-0.03	-1.47	0.14	-0.07	0.01	-0.03	-1.39	0.17	-0.06	0.01
Overvaluation		0.02	2.03	0.04	0.00	0.03	0.01	1.87	0.06	0.00	0.03
Total debt		0.04	1.84	0.07	0.00	0.09	0.04	1.80	0.07	0.00	0.09
	over GDP
Short-term		0.12	0.49	0.63	-0.35	0.58	0.13	0.53	0.60	-0.35	0.60
	debt over
	reserves
Real growth		-0.04	-0.91	0.37	-0.13	0.05	-0.04	-0.93	0.35	-0.14	0.05
	rate
Inflation							0.00	2.40	0.02	0.00	0.00
Constant		-2.16	-1.74	0.08	-4.59	0.27	-2.26	-1.75	0.08	-4.80	0.28
Wald x2 (5)		8.4					41.6
	and (6)

Source: Authors’ calculations. Note: GEE logit population-averaged model, correlation exchangeable, Huber-White estimation. 207 observations. CI refers to confidence intervals.

View Table

Table 10.

Regression Results Using Default Definition, Subsample for 1994-2002

					95 Percent					95 Percent
Defaults		Coeff.	Z	P>|z|	CI		Coeff.	Z	P>|z|	CI
Openness		-0.03	-1.47	0.14	-0.07	0.01	-0.03	-1.39	0.17	-0.06	0.01
Overvaluation		0.02	2.03	0.04	0.00	0.03	0.01	1.87	0.06	0.00	0.03
Total debt		0.04	1.84	0.07	0.00	0.09	0.04	1.80	0.07	0.00	0.09
	over GDP
Short-term		0.12	0.49	0.63	-0.35	0.58	0.13	0.53	0.60	-0.35	0.60
	debt over
	reserves
Real growth		-0.04	-0.91	0.37	-0.13	0.05	-0.04	-0.93	0.35	-0.14	0.05
	rate
Inflation							0.00	2.40	0.02	0.00	0.00
Constant		-2.16	-1.74	0.08	-4.59	0.27	-2.26	-1.75	0.08	-4.80	0.28
Wald x2 (5)		8.4					41.6
	and (6)

Source: Authors’ calculations. Note: GEE logit population-averaged model, correlation exchangeable, Huber-White estimation. 207 observations. CI refers to confidence intervals.

Table 11.

Regression Results Using PesSy Indicator, Subsample for 1994-2002

Source: Authors’ calculations. Note: GEE logit population-averaged model, correlation exchangeable, Huber-White estimation. 207 observations. CI refers to confidence intervals.

Table 11.

Regression Results Using PesSy Indicator, Subsample for 1994-2002

PesSy					95 Percent					95 Percent
	indicator	Coeff.	Z	P>|z|	CI		Coeff.	Z	P>|z|	CI
Openness		-0.02	-1.23	0.22	-0.05	0.01	-0.02	-1.09	0.28	-0.05	0.01
Overvaluation		0.02	1.83	0.07	0.00	0.04	0.01	1.50	0.13	0.00	0.03
Total debt		0.06	3.31	0.00	0.02	0.09	0.06	3.32	0.00	0.02	0.09
	over GDP
Short-term		0.34	1.89	0.06	-0.01	0.70	0.39	2.00	0.05	0.01	0.76
	debt over
	reserves
Real growth		0.01	0.17	0.87	-0.09	0.10	0.00	0.08	0.94	-0.10	0.10
	rate
Inflation							0.00	3.87	0.00	0.00	0.00
Constant		-3.53	-3.29	0.00	-5.64	-1.43	-3.84	-3.40	0.00	-6.05	-1.62
Wald x2 (6)		29.4					59.5
	and (7)

Source: Authors’ calculations. Note: GEE logit population-averaged model, correlation exchangeable, Huber-White estimation. 207 observations. CI refers to confidence intervals.

View Table

Table 11.

Regression Results Using PesSy Indicator, Subsample for 1994-2002

PesSy					95 Percent					95 Percent
	indicator	Coeff.	Z	P>|z|	CI		Coeff.	Z	P>|z|	CI
Openness		-0.02	-1.23	0.22	-0.05	0.01	-0.02	-1.09	0.28	-0.05	0.01
Overvaluation		0.02	1.83	0.07	0.00	0.04	0.01	1.50	0.13	0.00	0.03
Total debt		0.06	3.31	0.00	0.02	0.09	0.06	3.32	0.00	0.02	0.09
	over GDP
Short-term		0.34	1.89	0.06	-0.01	0.70	0.39	2.00	0.05	0.01	0.76
	debt over
	reserves
Real growth		0.01	0.17	0.87	-0.09	0.10	0.00	0.08	0.94	-0.10	0.10
	rate
Inflation							0.00	3.87	0.00	0.00	0.00
Constant		-3.53	-3.29	0.00	-5.64	-1.43	-3.84	-3.40	0.00	-6.05	-1.62
Wald x2 (6)		29.4					59.5
	and (7)

Source: Authors’ calculations. Note: GEE logit population-averaged model, correlation exchangeable, Huber-White estimation. 207 observations. CI refers to confidence intervals.

V. Conclusion

In this paper, we propose a definition of debt crises that complements the usual default definition. Because there were very few defaults on emerging market bonds in the 1990s in spite of a succession of turbulent foreign debt servicing episodes, we conclude that defining debt crises as defaults is too strict as an indicator of foreign debt incapacity. We therefore propose a measure that attempts to capture the evolution of capital markets from an environment dominated by bank loans to one in which bond markets have become increasingly important.

We define debt crises as events either when there is a default or when secondary-market bond spreads are higher than a critical threshold. We show, using extreme value theory and kernel density estimation, that a threshold of 1,000 bps does represent a statistically significant critical threshold. In practice, this threshold is often used by market participants.

We find that our definition accurately captures debt-servicing difficulties in the period from 1975 to 2002 and captures such difficulties better than the usual default definition, especially in the period after 1994. More precisely, we find that when our definition is used, the typical determinants of bank loan defaults in the 1980s still have predictive power for debt-servicing difficulties—on both bank loans and bonds—in the period from 1994 to 2002.¹⁵ In contrast, the standard definition of default implies much worse out-of-sample performance. In addition, we find that liquidity indicators are significant in explaining our definition of debt crises, although they do not play any role in explaining defaults in the period from 1994 to 2002.